linear algebraic equation help

Trying to use the following equations to find V for all pipes when ∑Ploss = 103kPa.

Pipe 1 flows into pipe 2 & 3 which are parallel then both flow into pipe 4.

∑Ploss is the same whether line 1, 2, 4 or 1,3,4 is taken.

Q1 = Q2 + Q3 = Q4.

Pressure loss in each pipe is, Ploss = (f*rho (L/D) )*(V^2/2).

Ploss across pipes in parallel is the same.

I want to iterate until the values of V do not change significantly from one iteration to another. To “linearise” the system of equations, I want to treat any term including V^2 as Vold ×V, where Vold is the value from the previous iteration. To ensure that the solution converges, I want to use an “under-relaxation factor” 0 < α< 1:

V = αVnew + (1-α)Vold

where Vnew is the value that is computed from the set of equations.

Hope that makes sense to someone

     D = zeros(4,1);D(0.1,1),D(0.2,1),D(0.05,1),D(0.15,1);
     L = zeros(4,1);L(10,1),L(3,1),L(4,1),L(8,1);
     %D1 = 0.1; L1 = 10; 
     %D2 = 0.2; L2 = 3; 
     %D3 = 0.05; L3 = 4; 
     %D4 = 0.15; L4 = 8; 
     %
     A = 0.25*pi.*D^2; 
     e = 0.0015e-3; 
     rho = 998; 
     nu = 1.01e-6; 
     eoverD = e./D;
     Ploss_total = 303.9e3; %Total Pressure Change
     %
     %Reynolds Number
      Re = (V.*D) / nu;
      if Re < 2300
      f = 64 / Re;
      else
      colebrook = @(x) 1/sqrt(x)+2*log10(eoverD/3.7 + 2.51/Re/sqrt(x));
      f = fzero(colebrook,0.01);
      end

[Marc]

Just a couple of comments.

In Matlab, I would think it would be easier to define your pipes diameters and length, along with everything else as vectors.

So instead of having 4 variables, D1, D2, etc. have D =zeros(4,1); and then fill in D(1,1), D(2,1), etc. etc.

Although I may have missed something, when you are calculating the Reynolds number, where did you define D or V or is this in your explanation and you want us to fill in the code?

Last comment, although I have many more, eoverD appears to be 4 elements. When you define colebrook function, do you want this to spit out 4 elements? If so, then you will probably want to replace the / with ./ and check the * if you need a .* ?

[harley]

thanks for your time, have made a couple edits as suggested above. I can have a separate initial V for each pipe and then iteratively adjusting the friction factor and changing the velocity using eqn.1 V = αVnew + (1-α)Vold in each iteration, (also making sure that Q1=Q2+Q3=Q4 in each iteration). In eqn 1 the V becomes the Vold in the next iteration. Re and f has to be calculated each time as the new V is calculated.